Topic 5: Understand and Use Ratio and Rate
Content Area: MathCourse(s): Math 6
Time Period: JanFeb
Length: 11-13 Days
Status: Published
Title Section
Department of Curriculum and Instruction
Belleville Public Schools Curriculum Guide
Math, 6th Grade
Topic 5
Belleville Board of Education
102 Passaic Avenue
Belleville, NJ 07109
Prepared by: Teacher, Morgan Chapman
Dr. Richard Tomko, Ph.D., M.J., Superintendent of Schools
Dr. Giovanni Cusmano, Director of Elementary Education K - 8
Mr. George Droste, Director of Secondary Education
Board Approved:7/16/2018
Unit Overview
Topic 5 Unit overview:
Topic 5 focuses on developing an understanding of ratios and rates and the way that they can be used to solve problems.
Enduring Understanding
Enduring understandings:
Understand ratios
Generate equivalent ratios
Compare ratios
Represent and graph ratios
Understand rates and unit rates
Compare unit rates
Solve unit rate problems
Ratio reasoning: Convert customary units
Ratio reasoning: Convert metric unitsEssential Questions
Essential Question: What are ratios and rates? How can you use ratios and rates to describe quantities and
solve problems?
Exit Skills
By the end of Topic 5 students should be able to:
Understand ratios
Generate equivalent ratios
Compare ratios
Represent and graph ratios
Understand rates and unit rates
Compare unit rates
Solve unit rate problems
Ratio reasoning: Convert customary units
Ratio reasoning: Convert metric units
Relate customary and metric unitsNew Jersey Student Learning Standards (NJSLS-S)
MA.6.RP.A.2 Understand the concept of a unit rate �/� associated with a ratio �:� with � ≠ 0, and use rate language in the context of a ratio relationship.
MA.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
MA.6.RP.A.3a Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MA.6.RP.A.3b Solve unit rate problems including those involving unit pricing and constant speed. MA.6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities.
MA.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Interdisciplinary Connections
TECH.8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. TECH.8.1.8.A.CS1 Understand and use technology systems.
Learning Objectives
Learning Objectives for Topic 5:
Use ratios to decribe the relationship between two quantities
Use bar diagrams and double number line diagrams to model ration relationships
Use multiplication and division to find equivalent ratios
Solve problems by finding equivalent ratios
Use ratio tables to compare ratios
Compare ratios to solve problems
Represent equivalent ratios on graphs
Use ratios tables and graphs to solve problems
Use rates to describe ratios in which the terms have different units
Use rates and unit rates to solve problems.
Use ratio reasoning to compare rates and solve problems
Use unit rates to solve problems involving constant speed
Use unit rates to solve problems involving unit price
Solve unit rate problems using an equation
Use mathematical modeling to represent a problem situation and to propose a solution
Test and verify the appropriateness of their math needs
Explain why the results from their mathematical models may not align exactly to the problem situation
Use ratio reasoning and conversion factors to convert customary/metric units of measureSuggested Activities & Best Practices
Topic 5 STEM Project:
the number of teeth each gear has. They use the engineering design process to design a set of gears for bicycle considering incline of terrain.
Evidence of Student Learning - Checking for Understanding (CFU)
• Admit Tickets .
• Anticipation Guide .
• Common benchmarks .
• Compare & Contrast .
• Create a Multimedia Poster .
• Define . • Describe . • Evaluate . • Evaluation rubrics . • Exit Tickets . • Explaining .
• Fist- to-Five or Thumb-Ometer .
• Illustration . • Journals . • KWL Chart . • Newspaper Headline . • Outline . • Question Stems . • Quickwrite . • Quizzes .
• Red Light, Green Light .
• Self- assessments .
• Socratic Seminar .
• Study Guide .
• Teacher Observation Checklist .
• Think, Pair, Share .
• Think, Write, Pair, Share .
• Unit tests .
Primary Resources & Materials
EnVision Math 2.0
Alignment to 21st Century Skills & Technology
CRP.K-12.CRP2 Apply appropriate academic and technical skills. CRP.K-12.CRP11 Use technology to enhance productivity.
CRP.K-12.CRP8 Utilize critical thinking to make sense of problems and persevere in solving them. CRP.K-12.CRP10 Plan education and career paths aligned to personal goals.
CRP.K-12.CRP12 Work productively in teams while using cultural global competence.
21st Century Skills/Interdisciplinary Themes
Upon completion of this section, please remove all remaining descriptions, notes, outlines, examples and/or illustrations that are not needed or used.
Please list only the 21st Century/Interdisciplinary Themes that will be incorporated into this unit.
• Communication and Collaboration .
• Creativity and Innovation .
• Critical thinking and Problem Solving .
• ICT (Information, Communications and Technology) Literacy .
• Information Literacy .
• Life and Career Skills .
• Media Literacy .
Differentiation
Differentiations:
Small group instruction
Small group assignments
Extra time to complete assignments
Pairing oral instruction with visuals
Repeat directions
Use manipulatives
Center-based instruction
Token economy
Study guides
Teacher reads assessments allowed
Rephrase written directions
Multisensory approaches
Additional time
Preview vocabulary
Preview content & concepts
Story guides
Behavior management plan
Highlight text
Student(s) work with assigned partner
Visual presentation
Assistive technology
Auditory presentations
Large print edition
Dictation to scribe
Small group setting Hi-Prep Differentiations:
Alternative formative and summative assessments
Choice boards
Games and tournaments
Group investigations
Guided Reading
Independent research and projects
Interest groups
Learning contracts
Leveled rubrics
Literature circles
Multiple intelligence options
Multiple texts
Personal agendas
Project-based learning
Problem-based learning
Stations/centers
Think-Tac-Toes
Tiered activities/assignments
Tiered products
Varying organizers for instructions Lo-Prep Differentiations
Choice of books or activities
Cubing activities
Exploration by interest
Flexible grouping
Goal setting with students
Jigsaw
Mini workshops to re-teach or extend skills
Open-ended activities
Think-Pair-Share
Varied journal prompts
Varied supplemental materialsIntervention Strategies
• allowing students to correct errors (looking for understanding) .
• teaching key aspects of a topic. Eliminate nonessential information .
• allowing products (projects, timelines, demonstrations, models, drawings, dioramas, poster boards, charts, graphs, slide shows, videos, etc.) to demonstrate student’s learning
.
• allowing students to select from given choices .
• allowing the use of note cards or open-book during testing .
• collaborating (general education teacher and specialist) to modify vocabulary, omit or modify items to reflect objectives for the student, eliminate sections of the test, and determine how the grade will be determined prior to giving the test.
.
• decreasing the amount of workpresented or required .
• having peers take notes or providing a copy of the teacher’s notes .
• marking students’ correct and acceptable work, not the mistakes .
• modifying tests to reflect selected objectives .
• providing study guides .
• reducing or omitting lengthy outside reading assignments .
• reducing the number of answer choices on a multiple choice test .
• tutoring by peers .
• using authentic assessments with real-life problem-solving .
• using true/false, matching, or fill in the blank tests in lieu of essay tests .
• using videos, illustrations, pictures, and drawings to explain or clarify .
Special Education Learning
• printed copy of board work/notes provided .
• additional time for skill mastery .
• assistive technology .
• behavior management plan .
• Center-Based Instruction .
• computer or electronic device utilizes .
• extended time on tests/ quizzes .
• have student repeat directions to check for understanding .
• highlighted text visual presentation .
• modified assignment format .
• modified test content .
• modified test format .
• modified test length .
• multiple test sessions .
• multi-sensory presentation .
• preferential seating .
• preview of content, concepts, and vocabulary .
• reduced/shortened reading assignments .
• Reduced/shortened written assignments .
• secure attention before giving instruction/directions .
• shortened assignments .
• student working with an assigned partner .
• teacher initiated weekly assignment sheet .
• Use open book, study guides, test prototypes .
English Language Learning (ELL)
• teaching key aspects of a topic. Eliminate nonessential information .
• using videos, illustrations, pictures, and drawings to explain or clarif .
• allowing products (projects, timelines, demonstrations, models, drawings, dioramas, poster boards, charts, graphs, slide shows, videos, etc.) to demonstrate student’s learning;
.
• allowing students to correct errors (looking for understanding) .
• allowing the use of note cards or open-book during testing .
• decreasing the amount of workpresented or required .
• having peers take notes or providing a copy of the teacher’s notes .
• modifying tests to reflect selected objectives .
• providing study guides .
• reducing or omitting lengthy outside reading assignments .
• reducing the number of answer choices on a multiple choice test .
• tutoring by peers .
• using computer word processing spell check and grammar check features .
